Continuously Crossing u=z in the H3+ Boundary CFT

For AdS boundary conditions, we give a solution of the H3+ two point function involving degenerate field with SL(2)-label b^{-2}/2, which is defined on the full (u,z) unit square. It consists of two patches, one for z<u and one for u<z. Along the u=z "singularity", the solutions from both patches are shown to have finite limits and are merged continuously as suggested by the work of Hosomichi and Ribault. From this two point function, we can derive b^{-2}/2-shift equations for AdS_2 D-branes. We show that discrete as well as continuous AdS_2 branes are consistent with our novel shift equations without any new restrictions.Comment: version to appear in JHEP - 12 pages now; sign error with impact on some parts of the interpretation fixed; material added to become more self-contained; role of bulk-boundary OPE in section 4 more carefully discussed; 3 references adde

A transient network of telechelic polymers and microspheres : structure and rheology

We study the structure and dynamics of a transient network composed of droplets of microemulsion connected by telechelic polymers. The polymer induces a bridging attraction between droplets without changing their shape. A viscoelastic behaviour is induced in the initially liquid solution, characterised in the linear regime by a stretched exponential stress relaxation. We analyse this relaxation in the light of classical theories of transient networks. The role of the elastic reorganisations in the deformed network is emphasized. In the non linear regime, a fast relaxation dynamics is followed by a second one having the same rate as in the linear regime. This behaviour, under step strain experiments, should induce a non monotonic behaviour in the elastic component of the stress under constant shear rate. However, we obtain in this case a singularity in the flow curve very different from the one observed in other systems, that we interpret in terms of fracture behaviour.Comment: 9 pages, 4 figure

Habitual Fluid Intake Does Not Affect Sleep Parameters in Young Women.

Sleep is essential for optimal physical performance, cognitive function, recovery, and overall health. Similarly, hydration status has been shown to influence physical and cognitive functions. Dehydration can lead to impaired cognition and possibly impaired sleep. However, the effect of habitual total water intake (TWI) on sleep and recovery measures have not been examined. PURPOSE: To examine the effect of TWI on sleep and recovery measures in young women. METHODS: Twenty-two young women (age: 22.8±4.6 yrs; body mass: 60.0±9.5 kg; height: 164.6±6.1 cm) collected fluid intake and food consumption information across a 5 day period, and average TWI was calculated based on them. Then, participants were categorized in either High Drinker (HD; ³ 2.5L/day; n=13; age: 23.0±3.6 yrs) or Low Drinker (LD; £ 1.6 L/day; n=9; age: 23±3yrs). Sleep and recovery measures were collected using a wearable sleep-tracking device that participants wore for 5 consecutive days. Sleep and recovery measures were compared between HD and LD, using a two-tailed independent t-test and effect sizes (ES). ES were identified as either small (0.2-0.49), medium (0.5-0.79), and large (\u3e0.8). RESULTS: No significant differences were found in resting heart rate (HD: 63.7±4.6 bpm, LD: 61.9± 5.2 bpm; p=0.40), heart rate variability (HD: 58.2±14.1 ms, 69.6±40.9 ms; p=0.44), slow wave sleep (SWS) (HD: 1.5±0.4 hrs, LD: 1.4±0.3 hrs; p=0.55), SWS percentage (HD: 19.3±3.8 %, LD: 18.7±3.7 %; p=0.17) sleep consistency (HD: 65.2±15.6 %, LD: 63.3±7. 3%; p=0.71), and sleep efficiency (HD: 90.5±3.1 %, LD: 90.4±2.0 %; p=0.91). While there were no statistical differences, rapid eye movement (REM) sleep (HD: 2.0±0.4 hrs, LD: 1.6±0.7 hrs; p=0.17) and REM percentage (HD: 26.1±3.8 %, LD: 21.5±7.8 %; p=0.13) displayed the largest differences, with REM indicating a medium ES (d=0.70) and REM percentage having a large ES (d=0.80). CONCLUSION: Habitual fluid intake might not impact sleep measurement. However, based on ES, REM sleep and REM percentage potentially display a trend. Still, more research is necessary to further determine any correlations

One pendulum to run them all

The analytical solution for the three-dimensional linear pendulum in a rotating frame of reference is obtained, including Coriolis and centrifugal accelerations, and expressed in terms of initial conditions. This result offers the possibility of treating Foucault and Bravais pendula as trajectories of the same system of equations, each of them with particular initial conditions. We compare them with the common two-dimensional approximations in textbooks. A previously unnoticed pattern in the three-dimensional Foucault pendulum attractor is presented

Impact of Habitual Water Intake on Muscle Quality and Total Body Water-A Pilot Study

Proper hydration is essential for critical health and performance functions, such as muscle function and body fluid balance. The effect of acute hydration status has been studied on health and muscle performance; however, the effect of habitual water intake on muscle quality and total body water between high and low consumption has not been examined. PURPOSE: To determine the impact of habitual water intake on muscle quality and total body water. METHODS: Eleven women (age: 27.6±7.9 years; mass: 60.3±10.8 kg) provided a five-day dietary food log to categorize them into HIGH or LOW daily total water intake (TWI). TWI values \u3e2.5-3.3 L/day (HIGH) or \u3c 0.7-1.6 L/day (LOW) were used to determine groups. Bioelectrical impedance analysis (BIA) and ultrasound images were obtained to assess overall muscle quality and total body fluid balance between the two groups. Analysis of ultrasound images using ImageJ determined length (cm), cross-sectional area (CSA), and muscle quality through echo intensity (EI) of the participant’s right and left rectus femoris (RF). An independent sample T-Test and effect sizes (ES) were used to assess differences between HIGH and LOW. RESULTS: Due to this study being a pilot study, there was no significant differences in right RF length between LOW (1.44±0.22 cm) and HIGH (1.22±0.24 cm, p=0.153) with a large effect size of (ES=0.98). There were no significant differences in left RF length (p=0.861) between HIGH (1.46±0.28 cm) and LOW (1.42±0.32) groups with a trivial effect size (ES=0.11). Right RF CSA had non-significant differences between LOW (3.72±1.18 cm2) and HIGH (2.95±1.05 cm2, p=0.309) with medium effect (ES=0.68). There were no differences in CSA-left between HIGH (3.63 ± 1.06 cm) and LOW (3.83±1.44, p=0.816, ES=0.15). Right RF muscle quality also had a medium effect size (ES=0.78) between HIGH (135.30±21.82 A.U) and LOW (117.71±23.10 A.U). Muscle quality of the left RF had a small effect size (ES=0.26) between LOW (118.29±22.18 A.U) and HIGH (125.97±39.47 A.U, p=0.684). While there was no statistical difference due to the power (p=0.163), total body water (TBW) percentage (%) was greater in HIGH (53.9±1.5%) compared to LOW (50.6±5.4%, ES= 0.75) with medium effects. HIGH and LOW demonstrated no statistical difference (p=0.579) with a small effect size (ES=0.36) between ECF% and ICF%, respectively (41.00±0.72%, 41.39±1.20%; 59.00±0.72%, 58.61±1.20%). CONCLUSION: Despite no significant differences, based on ES, HIGH habitual water intake increases TBW% than LOW. Further data must be collected to draw definitive conclusions; however, these results suggest skeletal muscle quality is high with LOW habitual water intake

Spherical functions on the de Sitter group

Matrix elements and spherical functions of irreducible representations of the de Sitter group are studied on the various homogeneous spaces of this group. It is shown that a universal covering of the de Sitter group gives rise to quaternion Euler angles. An explicit form of Casimir and Laplace-Beltrami operators on the homogeneous spaces is given. Different expressions of the matrix elements and spherical functions are given in terms of multiple hypergeometric functions both for finite-dimensional and unitary representations of the principal series of the de Sitter group.Comment: 40 page

Projective dynamics and classical gravitation

Given a real vector space V of finite dimension, together with a particular homogeneous field of bivectors that we call a "field of projective forces", we define a law of dynamics such that the position of the particle is a "ray" i.e. a half-line drawn from the origin of V. The impulsion is a bivector whose support is a 2-plane containing the ray. Throwing the particle with a given initial impulsion defines a projective trajectory. It is a curve in the space of rays S(V), together with an impulsion attached to each ray. In the simplest example where the force is identically zero, the curve is a straight line and the impulsion a constant bivector. A striking feature of projective dynamics appears: the trajectories are not parameterized. Among the projective force fields corresponding to a central force, the one defining the Kepler problem is simpler than those corresponding to other homogeneities. Here the thrown ray describes a quadratic cone whose section by a hyperplane corresponds to a Keplerian conic. An original point of view on the hidden symmetries of the Kepler problem emerges, and clarifies some remarks due to Halphen and Appell. We also get the unexpected conclusion that there exists a notion of divergence-free field of projective forces if and only if dim V=4. No metric is involved in the axioms of projective dynamics.Comment: 20 pages, 4 figure

The helium atom in a strong magnetic field

We investigate the electronic structure of the helium atom in a magnetic field b etween B=0 and B=100a.u. The atom is treated as a nonrelativistic system with two interactin g electrons and a fixed nucleus. Scaling laws are provided connecting the fixed-nucleus Hamiltonia n to the one for the case of finite nuclear mass. Respecting the symmetries of the electronic Ham iltonian in the presence of a magnetic field, we represent this Hamiltonian as a matrix with res pect to a two-particle basis composed of one-particle states of a Gaussian basis set. The corresponding generalized eigenvalue problem is solved numerically, providing in the present paper results for vanish ing magnetic quantum number M=0 and even or odd z-parity, each for both singlet and triplet spin symmetry. Total electronic energies of the ground state and the first few excitations in each su bspace as well as their one-electron ionization energies are presented as a function of the magnetic fie ld, and their behaviour is discussed. Energy values for electromagnetic transitions within the M=0 sub space are shown, and a complete table of wavelengths at all the detected stationary points with respect to their field dependence is given, thereby providing a basis for a comparison with observed ab sorption spectra of magnetic white dwarfs.Comment: 21 pages, 4 Figures, acc.f.publ.in J.Phys.

Projective dynamics and first integrals

We present the theory of tensors with Young tableau symmetry as an efficient computational tool in dealing with the polynomial first integrals of a natural system in classical mechanics. We relate a special kind of such first integrals, already studied by Lundmark, to Beltrami's theorem about projectively flat Riemannian manifolds. We set the ground for a new and simple theory of the integrable systems having only quadratic first integrals. This theory begins with two centered quadrics related by central projection, each quadric being a model of a space of constant curvature. Finally, we present an extension of these models to the case of degenerate quadratic forms.Comment: 39 pages, 2 figure

Superposition of Weyl solutions: The equilibrium forces

Solutions to the Einstein equation that represent the superposition of static isolated bodies with axially symmetry are presented. The equations nonlinearity yields singular structures (strut and membranes) to equilibrate the bodies. The force on the strut like singularities is computed for a variety of situations. The superposition of a ring and a particle is studied in some detailComment: 31 pages, 7 figures, psbox macro. Submitted to Classical and Quantum Gravit